Gabor frames for rational functions

• 成果类型: Article
• 署名作者: Belov, Yurii; Kulikov, Aleksei; Lyubarskii, Yurii
• 署名单位: Norwegian University of Science & Technology (NTNU)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01151-8
• 发表日期: 2023
• 页码: 431-466
• 关键词: weyl-heisenberg frames; density theorems; interpolation

摘要

We study the frame properties of the Gabor systems G(g; alpha, beta) := {e(2 pi i beta mx) g(x - an)} m,n is an element of Z. In particular, we prove that forHerglotzwindows g such systems always form a frame for L-2(R) if alpha, beta > 0, alpha beta <= 1. For general rationalwindows g is an element of L-2(R) we prove that G(g; alpha, beta) is a frame for L-2(R) if 0 < alpha, beta, alpha beta < 1, alpha beta is not an element of Q and (g) over bar(xi) not equal 0, xi > 0, thus confirming Daubechies conjecture for this class of functions. We also discuss some related questions, in particular sampling in shift-invariant subspaces of L-2(R).